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Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks

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Abstract

The outbreak of corona virus disease 2019 has profoundly affected people’s way of life. It is increasingly necessary to investigate epidemics over social networks. This paper studies susceptible-infected-removed (SIR) epidemics via the semi-tensor product. First, a formal susceptible-infected-removed epidemic dynamic model over probabilistic dynamic networks (SIRED-PDN) is given. Based on an evolutionary rule, the algebraic form for the dynamics of individual states and network topologies is given, respectively. Second, the SIRED-PDN can be described by a probabilistic mix-valued logical network. After providing an algorithm, all possible final spreading equilibria can be obtained for any given initial epidemic state and network topology by seeking attractors of the network. And the shortest time for all possible initial epidemic state and network topology profiles to evolve to the final spreading equilibria can be obtained by seeking the transient time of the network. Finally, an illustrative example is given to show the effectiveness of our model.

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Authors and Affiliations

  1. College of Artificial Intelligence, Nankai University, Tianjin, 300350, China

    Hongxing Yuan, Zengqiang Chen, Rui Zhu & Zhongxin Liu

  2. School of Artificial Intelligence, Tiangong University, Tianjin, 300387, China

    Zhipeng Zhang

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  1. Hongxing Yuan
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Correspondence to Zhongxin Liu.

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The authors declare that there is no conflict of financial or non-financial interests that are directly or indirectly related to the publication of this paper.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 61973175, 62203328), the Tianjin Natural Science Foundation (Nos. 20JCYBJC01060, 21JCQNJC00840) and the General Terminal IC Interdisciplinary Science Center of Nankai University.

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Yuan, H., Chen, Z., Zhang, Z. et al. Algebraic form and analysis of SIR epidemic dynamics over probabilistic dynamic networks. Control Theory Technol. 21, 602–611 (2023). https://doi.org/10.1007/s11768-023-00143-0

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